Falsifiability is a fundamental property of a statement of it being possible to have counter-examples to (the search for these counter-examples is called falsification). According to Karl Popper, claims that are not falsifiable are considered to be outside the realm of science. This criterion is accepted by most of the worldwide scientific community.
It is not a requirement of falsifiability that there be a current means of falsifying the theory. It must simply be logically possible that an observation or experiment could have done so, if it were not true. In cases where the theory is shown to be true, such as the Theory of Evolution, the means of falsification are exhaustively demonstrated to be incorrect.
Special creation is not falsifiable. Every theoretical circumstance is consistent with the idea that god specially created every species. Any possible evidence to the contrary would simply change god's role in creation, but would not falsify the theory.
The Theory of Evolution is falsifiable. Had the fossil record been found to be static, it would have shown that species have not evolved. Had a mechanism been found that prevents, and has always prevented, genetic mutations from accumulating or being inherited, it would make evolution impossible. However, the opposite is true in both cases.